This invention relates to a sputtering apparatus simulation method and, in particular, to a sputtering apparatus simulation method reflecting the influence of temperature rise during sputtering.
As one of conventional sputtering apparatus simulation methods reflecting the influence of temperature rise during sputtering, a simulation method utilizing the Monte Carlo method is known (H. Yamada et. al., 1994, IEDM Tech. Digest, pages 553-556). Referring to FIG. 1, a sputter particle is emitted from a target 11 of a sputtering apparatus, passes through a collimator 12, and reaches a wafer 13. In order to obtain an orbit 14 of the particle, calculation is made of a generating position, an emission angle, and energy of the particle by the use of a random number. Subsequently, with reference to the above-mentioned values, a collision point 16 of the particle emitted from an emission point 15 is calculated assuming the Poisson distribution.
Next, a scattering angle of a sputter particle due to the collision is calculated by rigid-sphere approximation with reference to the result of elastic scattering calculation in the central force field. Herein, it is assumed that velocity distribution of a surrounding gas particle which collides with the sputter particle exhibits the Maxwell distribution. In the above-mentioned manner, the orbit 14 of the sputter particle reaching the wafer 13, which is a silicon substrate, is calculated
When the sputtering rate or the surrounding gas pressure is high, the temperature of the surrounding gas increases during the sputtering and the temperature has a nonuniform distribution. However, the conventional simulation method assumes that the temperature of the surrounding gas is constant during the sputtering. Thus, the influence of the temperature rise or the temperature distribution can not be reflected at all.
In order to reflect the above-mentioned influence, use may be made of a direct Monte Carlo method. According to this method, a large number of particles are generated in the sputtering apparatus and calculation is made of the orbit and the collision for each particle. However, the direct Monte Carlo method requires the calculation for such a large number of particles, the calculation time inevitably becomes long.